Introduction

More than a decade has passed since the discovery of high-temperature superconductivity
(HTS), but it still remains a challenge for physicists to set off the right
model which would explain the main experimental features of the new superconductors.
In majority of theoretical models of HTS, it is assumed that the normal and
superconducting state properties of the layered high-Tc
cuprates derive mainly from the properties of the CuO2 planes,
while the other structural components in the unit cell act simply as charge
reservoirs. The interlayer coupling has largely been considered as the mechanism
of controlling the carrier concentration in the CuO2 planes.

The c-axis (or out-of-plane) coupling has become especially important
when the interlayer tunneling model of HTS
has been developed. In this model, the energy gain that drives the formation
of the pairs is associated with a decrease of the kinetic energy due to the
easy motion of the pairs accompanied by the impeded single-particle tunneling
along the c-axis.

Another important question is whether the normal state out-of-plane transport
is coherent or not, and what is the origin of the "semiconducting" c-axis
resistivity in the cuprates. All theories of out-of-plane transport differ
in whether the zero-temperature state of cuprates is "metallic" with a finite
c-axis resistivity rc, or insulating
with an infinitely large rc. Major c-axis transport models have been
examined in the review article by Cooper and Gray.

The physics of vortices has become one of the most quickly developing part
of modern physics. HTS's with their large anisotropy and thermal fluctuations
represent a big research field where many new effects have become possible
to observe experimentally. A clear experimental evidence for melting of the
classic Abrikosov vortex lattice in a wide temperature range below superconducting
critical temperature Tc has verified a number of theories
and stimulated further experimental and theoretical studies.

Intrinsic Josephson effect (IJE) as a tunneling of the Cooper pairs between
adjacent CuO2 planes inside the highly anisotropic layered HTS
is an integral part of almost all theories on this subject and is of primary
importance for deriving the properties of the vortex system. It was experimentally
confirmed by Kleiner and Müller, that the intrinsic
tunneling of the Cooper pairs indeed takes place in Bi2Sr2CaCu2O8+d(Bi-2212) and other anisotropic single crystals
(Tl2Sr2Ca2Cu3O10+d(Tl-2223) and (PbyBi1-y)2Sr2CaCu2O8+d(Bi(Pb)-2212) ). In these experiments both dc
and ac Josephson effects have been observed. The current-voltage (I-V) characteristics
for current flow in the c-axis direction exhibited large hysteresis
and multiple branches. These results clearly showed that all the materials
behave like stacks of superconductor-insulator-superconductor (SIS) Josephson
junctions, see Figure below. The review
of all these observations and the present status of research regarding theoretical
understanding of the intrinsic Josephson effect has been given some time
ago. For an unsorted collection of recent works on intrinsic Josephson effect,
see this Reference.

The experimental discovery of IJE in HTS's is very important because it
sets in the limitations on possible theories of HTS and requires reassessment
of many works. Those experimental works which involve the c-axis tunneling
in highly anisotropic HTS but fail to demonstrate IJE clearly, should be
taken with discretion.

One of the important issues of HTS is its promising practical applications,
like three-terminal devices or SIS mixers. Attractive feature of HTS's, their
large energy gap in the quasiparticle excitation spectra implies that the
operational upper frequency for feasible HTS-devices may lie in the THz-region.
Since the discovery of HTS, there have been worldwide attempts to obtain
reproducible tunnel junctions of HTS materials for potential applications.
The most popular and most developed Josephson junctions use different types
of weak-link contacts between misoriented thin films of HTS, see discussion
on the different types of HTS Josephson junctions. Although there are some
signatures of SIS nature of, for instance, grain-boundary Josephson junctions,
a well-defined quasiparticle gap feature which is a signature of the elastic,
single-particle tunneling, is very seldom clearly observed. Moreover, the
nature of the weak contact between misoriented grains of HTS is still unclear.
Intrinsic Josephson junctions favorably stand out against other types of
HTS Josephson junctions by their naturally perfect structure in terms of
uniformity and reproducibility and their SIS character, which makes them
attractive for device applications.

Taking the simplified scheme alone, we make conclusion that the whole Bi-2212 single crystal is just one-dimensional array
of S-I-S Josephson junctions. We call such junctions as intrinsic because
they are inside the singler crystal. We also believe they are unique
and are the only example of naturally made Josephson junctions with extreme
degree of quality and uniformity. Such an array has a current-voltage
characteristic which consits of several branches when current is sweeping
back and forth from zero to a some maximum value. Each branch corresponds
to one, two, three etc. intrinsic Josephson junctions having switched to the
dissipative regime (quasiparticle state) with a finite voltage across each
of them, see Fig.2.

Fig.2. Schematic I-V's of a series array of five hysteretic SIS
Josephson junctions. Thick red lines mark the parts of branches that
are only seen in a constant-amplitude ac-current bias. Thin orange
parts can be traced out when the amplitude is modulated at another
(lower) frequency. Vg is the superconducting gap voltage. Note also
that there is no certain correspondence between branches and particular
junctions in the array, i.e. one and the same branch can result from
collective switching of different junctions at different periods of
ac-bias.

Fabrication techniques

In our experiments we use photolithography and Ar-ion- or chemical etching
to make small mesa structures on surfaces of Bi-2212 single crystals. Typically,
mesas are about 10x20 micron2 large and 15-300 Å high.
We usually make two contacts on each mesa, which allow making
four-probe measurements of the c-axis transport properties, see Fig. 3.

Fig.3. Different geometries of samples that can be used for
measurements of the c-axis transport properties. The major tool in
fabrication is Scotch tape, while Ar-ion etching allows for fine-tuning
of sizes. It is important to have a smooth surface both
after the cleavage and Ar-ion etching (left). We can do both 2-, 3-, or
4-probe measurements on the mesas by applying current to- (or measuring
voltage at) different contacts (bottom).

Properties

Pressure
dependence of the c-axis critical current

Motivation: The interlayer tunneling model (ILT) is one of the leading candidates for explaining
high-temperature superconductivity. In this model, the energy gain that drives
the formation of the pairs is associated with a decrease of the kinetic energy
due to the easy motion of the pairs accompanied by the impeded single-particle
tunneling along the c-axis. The model in its current version predicts an
increase of the condensation energy Ec proportionally to
the interlayer Josephson coupling t^2,
or to the inverse square of the c-axis penetration depth lc, or the c-axis critical current.
A conclusive experimental check of this prediction for different single-layer
high-Tc materials would provide a critical test of the ILT model.

We used hydrostatic pressure P < 1 GPa as a tool to change the
c-axis interlayer coupling of Bi2Sr1.5La0.5CuO6+x
(Bi-2201) and Bi-2212 single crystals, see Fig. 4. The pressure can
be applied in a simple pressure chamber, see the photo.

Fig. 4

Results.
The c-axis critical current of Bi-2212 (left) and Bi-2201(right), as
a measure of the interlayer coupling, drastically increases with pressure
(up to 270 %GPa-1), see Fig. 5.

Fig. 5

The superconducting critical temperature, on the contrary, only slightly
increases with a rate of ~ 2-6 % GPa-1, see Fig. 6, the inset.

Fig. 6

Conclusions.

All this implies that the CuO-interlayer coupling has little effect on
Tc in Bi-system, in contrast to the ILT model.

Intrinsic
Josephson junctions in a magnetic field

Measurements of the c-axis, out-of-plane, electrical transport properties
are of great importance in probing the vortex system properties of highly
anisotropic layered high-Tc (HTc) compounds, such as Bi2Sr2CaCu2O8
(2212-BSCCO). In such superconductors, vortex lines are formed from
vortex "pancakes" with circulating currents confined to the CuO2
planes. The pancakes interact with each other magnetically and via interlayer
Josephson coupling. In an ideal layered superconductor at low temperatures,
these interactions encourage pancakes to align perpendicular to the planes.
However, when the interlayer interactions are weak, thermal fluctuations
and local pinning centres cause misalignment. This leads to a loss in phase
coherence between adjacent pairs of superconducting planes and hence a reduction
in the critical current.

These orientations of the magnetic field, current,
and the c-axis were used in our experiments.

Temperature dependence of (a) the out-of-plane
resistances for the oxygen-annealed sample in a perpendicular magnetic field.
The inset shows an enlarged part of the dependence close to Tc.For comparison, we have also included
a single 6- T measurement for the argon-annealed sample which exhibits a
resistance peak almost twice as large as for the oxygen-annealed sample, whereas
the zero-field critical current at low temperatures is approximately halved.
This suggests an inverse relationship between the magnitude of the resistive
peak and the critical current density.

Despite the onset of resistance at low voltages above Tirr,
it is still possible to define a critical current in terms of the "excess
current" extrapolated to zero voltage, which varies smoothly through the melting
transition regime, as illustrated in Fig. 4. The somewhat surprising existence
of a critical current extending well into the liquid state is a consequence
of the attractive Josephson or magnetic coupling of pancakes between the
planes. This results in a thermally averaged, partial alignment of the pancakes,
as described by Koshelev. This also accounts for the persistence of the microwave
Josephson plasma resonance at temperatures well above the irreversibility
line.

(a) and (b): I-V characteristics
of the oxygen-annealed sample in the perpendicular magnetic field of 0.4 T
at T = 36 K and T = 70 K.

(c) Temperature dependence of the
c-axis critical current for perpendicular magnetic fields as indicated. Empty
symbols represent the "quasi-critical" current Ic* defined
in Fig. (b). Filled symbols correspond to the critical current Ic defined
using a 0.1 µV voltage criterion or from the critical current distribution
functions P(Ic). The lines drawn through the experimental
points are only intended as guides for the eye.

Below, we show the B-T phase diagram suggested by our measurements
for fields perpendicular to the ab-planes. The open symbols indicate
the temperature T* of the first peak in critical current (see above)
and the filled symbols the temperature Tirrmarking the
onsetof resistivity along
the c-axis. Over a relatively wide range of fields, Tirr µ ln(1/B^).

There appears to be a weak maximum in T* at small fields, while
at large fields it approaches the field-independent, 2D vortex lattice Kosterlitz-Thouless
melting transition, T2D. This is consistent with the suppression
of both Josephson and electromagnetic interlayer coupling at high fields,
so that the system becomes increasingly two-dimensional.

T* and Tirr define three regions of the B-T
phase-diagram. This involves two solid phases below Tirr,
where a zero voltage, true c-axis supercurrent is observed, and a
liquid phase above Tirr, where the c-axis conduction
is dissipative. T* may mark the temperature at which both C44
and C66, the elastic moduli of the vortex lattice, are
predicted to vanish. The phase between T* and Tirr
may represent a glassy state of vortices with long-range orientational
order; whereas the transition to a more conventional liquid state does not
occur until Tirr.

B-T- diagram of vortex phases for fields
perpendicular to the ab-planes suggested by our measurements. Empty symbols
represent the field dependence of the temperature T* at which the maximum
of Ic(B^,T)-dependence
is observed, see Fig. (c) above. The solid symbols represent the irreversibility
line Tirr(B^)
observed in different experiments:(? )- µSR measurements; (? )-melting
line from Ref. , where multi-terminal transport measurements in the flux-transformer
configuration have been made; (? ) and (+)- irreversibility line inferred
from the magnetization measurements of a 2212-BSCCO single crystal from the
same batch as those used in the present study (upper triangles and circles,
for the argon and oxygen annealed sample, respectively). Although the lines
are only guides for the eye, the irreversibility temperature seems to obey
a simple logarithmic dependence, Tirr(B^) ? -ln(B^), illustrated by the straight line in this
semi-logarithmic plot.

Although the rapid onset of a resistance at Tirr(B^)suggests a first-order melting transition,
as observed by Fuchs et al. at small fields, the absence of any qualitative
change in the I-V characteristics at the transition imply a second-order
or thermally broadened phase transition at these higher fields. Our measurements
suggest that there is little change in the correlation of flux pancakes in
the c-direction at the melting transition, with perhaps a significant
fraction of pancakes remaining strongly pinned at this transition. This could
also account for the slight increase of Ic*(T,B^) on increasing temperature above Tirr(B^) as such pancakes eventually become thermally
unpinned, enabling them to move more freely and hence to optimise their thermally
averaged alignment along the c-direction.

Heavy-ion irradiation

The c-axis critical current Ic(T,B), the resistance
Rc(T,B), and the detailed form of the I-V characteristics of
a number of mesas were measured as functions of temperature and perpendicular
magnetic field, before and after 5.8GeVPb-ion irradiation
with three different doses (2.5, 5, and 10x1010cm-2).
We note that although columnar defects produced by the irradiation penetrate
through the whole thickness of a single crystal, the measurements involve
only 10-15 CuO layers in the mesas.

Figure shows Rc(T) at different magnetic fields for two
samples before and after irradiation. First, it is seen (top panel) that
the increase of the resistance for one of the samples (No.1) in merely 5
T of the field strength is about 60 times the normal state resistance at
T=160K. Typically, we observe an increase of resistance of the order
of (10-12)Rc(160K) in 6-7T. We believe
that such a big magnetoresistance effect is due to an occasionally perfect
Bi-2212 crystal structure in the investigated mesa. Crystalline defects would
likely provide local electrical shorts between CuO planes, thus decreasing
the overall sub-gap resistance Rsgof an individual IJJ.
Recently, we have experimentally shown that Rsg sets an upper
limit of the magnetoresistance peak effect (MRPE) of a Bi2212 single crystal.After irradiation with a total dose of ions of 1011cm-2 (corresponding to a matching field
Bf=2T) MRPE is significantly suppressed
to a value of 20, see the inset of Fig.(top). For the second sample (No.2)
the change of the MRPE after irradiation is only 20%. This may be due to
a lower dose (Bf=1T) and to
a difference in sample quality (the MRPE for that sample was about 20Rc(160K)
prior to irradiation). The temperature of the zero-resistance state, Tc(B),
increased significantly after irradiation for both samples.

Figures show the magnetic field dependence of the critical current for two
samples after the irradiation with different doses (Bf=1 and 2T). All measurements were made on warming
in constant applied field after first cooling from above Tc(0)
in the field. First, Ic decreases rapidly with perpendicular
field, as predicted theoretically and observed by us in another work (see
the inset of Fig.(b)). It is clearly seen that at approximately 1/3 of the
matching field, the critical current starts to rise, reaches a maximum in
the range between 1/3 and 1/2 of Bf,
and then decreases again, but with a somewhat slower rate. The feature in
Ic(B) is clearly seen at T~ 30K. With increasing
temperature, it gets smeared and disappears on approaching Tc(B)
(irreversibility line). In addition to the maximum at B»1/3Bf,
there is no feature at B~Bf.

Sub-gap conductance and c-axis resistance in the normal state

We have experimentally demonstrated that the c-axis magnetoresistance
peak effect is determined by the sub-gap resistance of intrinsic Josephson
junctions in Bi2212. Given a Bi2212 single crystal, the effect may be predicted
from the c-axis current-voltage characteristics in zero
magnetic field. At high magnetic field H, the I-V characteristics
preserve their overall non-linear shape at the transition temperature Tc(H)<
Tc(0) suggesting a smooth change of the vortex system with
temperature. Observation of the gap feature below Tc(0)
at all µ0H<7 T means that the upper critical field
is not attained at these fields.

See also Fig. where the 60-fold increase
of resistance in the magnetic field of about 6 T was observed.

Intercalation

In Bi-2212 with rather poor thermal and electrical conductivity, the Joule
heating at high bias current may become essential, and a short-pulse technique may be needed to overcome such
a problem.

We have chosen another method, and have used intercalation
of the inert HgBr2-molecules to lengthen the c axis of the host
Bi-2212 single crystals, see Fig.7.
Correspondingly, the intrinsic tunneling barriers are becoming wider which
results in a drastic decrease of the c-axis critical current density.
In its turn, the heat-release during sweeping the current to reach the normal-state
tunneling parts of the current-voltage (I-V) characteristics drops off as
well.

Fig. 7

Remarkably enough, such an intervention does not change quality of resulting
I-V's , which usually consist in evenly spaced in voltage hysteretic quasi-particle
branches. The total number of the branches seen in I-V-plot tells one how
many intrinsic Josephson junctions (IJJ) are enclosed in the mesa, see the
Figure below.

Figure shows the normalized resistance
R for both the pristine Bi2212-, and HgBr2-Bi2212-mesas of the same areas
and heights. It is seen, that the overall shape of R(T)-dependence
and the characteristic temperature T* at which an upturn in R(T)-
dependence sets in upon cooling do not change. This implies that T*
is not affected by the coupling between the CuO2-bilayers. Pseudogap-feature in
Bi2212 is thus derived from the properties of the bilayers alone. See also
intrinsic spectroscopy of the pseudogap below.

The tunneling spectroscopy is particularly sensitive to the density of
states (DOS) at the Fermi level and therefore can be used to study any gap
in the quasiparticle excitation spectrum. The most common experimental
methods, STM and point-contact techniques are surface probes, and therefore
are affected by surface deterioration.

In our experiments we study the tunneling properties of Bi-2212 using the
so called intrinsic spectroscopy (Schlenga98),
for which such problems are unimportant. The atomic perfection of the naturally
occurring tunnel junctions in this material provides a reliable basis for
the tunneling spectroscopy inside the single crystal giving a high
degree of homogeneity and reproducibility.

Superconducting energy gap

The quasiparticle branches in Figure are having
a well defined gap feature. For instance, the slope of the first quasiparticle
branch is almost vertical at V»25
mV. The same applies for the last branch, too. Since it corresponds to all
9 IJJ in the quasiparticle state, one can deduce the average value of the
gap voltage per junction to be about the same 25 mV. Recalling the fact that
for the SIS-type Josephson junctions the gap feature is taking place at V»2D /e, we conclude
that D» 12-13 meV for tunneling in the c-axis
direction. This value is about one half of the value obtained from the scanning
tunneling microscopy (STM) data, or break-junction technique.

Several explanations have been suggested. The trivial heating explanation
(see Problems) implies that the temperature of the
mesa is increased up to about 0.6Tc due to the power dissipation
in the junctions. Assuming a BCS-like temperature dependence of the gap parameter,
one would see then a smaller than expected gap. On the other hand, the more
IJJ are going normal in the stack, the more heat power is released, and the
less gap voltage and the smaller separation in voltage between branches with
higher count numbers should be observed. It is contradicting the experiment,
where almost all branches in the I-V-characteristics are equidistant in voltage.

The non-equilibrium quasiparticle self-injection, which is typical for
stacks of tunnel junctions, can also cause the gap to decrease. Since the
thickness of each electrode of individual IJJ is about 3Å only, the
quasiparticles generated in one junction can easily penetrate others and change
the quasiparticle population. The competition between the rate of generating
of quasiparticles and their recombination rate determines the steady concentration
of quasiparticles and the operational gap parameter.

The proximity effects suggested (we97) could explain both the reduced value
of the gap parameter and its strong temperature dependence. If one assumes
that the bottle-neck for the current flow in the c-axis direction
resides in between adjacent BiO-layers, which can be metallic and even superconducting
due to proximity effects, then the actual schematics of intrinsic tunnel
junction is SS'-I-S'S rather than S-I-S. (S' here represents superconducting
BiO-plane with a smaller superconducting energy gap), see Structure. The reduced and strongly temperature
dependent energy gap has also been observed in angle-resolved-photoemission
(ARPES) experiments (Ma??).

The results on the reduced value of the c-axis energy gap were criticized
in the paper by Itoh \etal, where the authors also used the small-height
stacks on the surfaces of Bi-2212 single crystals. In their three-probe
measurements, Itoh \etal managed to reach the normal-state parts of the tunneling
I-V-characteristics for which there were no parts with negative dynamic resistance.
The S-shaped characteristics with heavy back-bending at the gap-voltage usually
witness to the heating in stacks. To further decrease the heating in contacts
to stacks the authors annealed them at 650ºC during 1h. Although the
diffusion of the silver into the stacks during the annealing had most likely
distorted the properties of the host material, it looks that the two works
differ mainly in measurement techniques, as whether the three- or four- probe
methods were used.

In the four-probe technique, where the current and potential leads are
separated by a distance of several microns, the non-equilibrium effects are
more prominent than in the three-probe measurements. Charge imbalance at
high bias current can initiate an additional voltage at the top of the stack
between potential and current leads. That is why it is seldom possible to
reach the normal state in the four-probe measurements without the back-bending
of the tunneling curves. Moreover, the high bias current accompanied by non-equilibrium
effects which are present in all cases, may destroy the weak superconductivity
of BiO planes and make the corresponding reduced gap unobservable. At low
currents, the results of three- and four- probe measurements are basically
similar, and the separation in voltage between the branches is the same 20-30
meV.

Pseudogap

Pseudo-gap (PG) in electronic excitation spectra is one of the very important
features of high-Tc (HTS) superconductors. Such a gap was reported
to exist in both underdoped and overdoped samples, and was observed to transform
into the superconducting gap (SG) upon cooling in a number of experiments

Figure shows the c-axis dynamic
conductance dI/dV(V) for HgBr2-Bi2212 at
different temperatures, obtained by differentiating the last branch corresponding
to all 14 IJJ being in the quasi-particle state. Both SG- and PG- features
are clearly resolved at T<Tc and are therefore
concluded to be independent phenomena. Moreover, the PG-feature does
not depend on temperature, while SG-voltage decreases with T and looses
its distinctiveness on approaching Tc. For slightly underdoped
HgBr2-Bi2212, SG-feature could be traced closer to Tc
than for the similar overdoped crystals. Note also that, being re-scaled
down to areas 5x5 Å2 which may be presumed for STM, the
conductance results in even smaller than in STM values 10-12 Ohm-1.
This proves the high quality of intrinsic tunnel junctions.

Problems

The main problem with intrinsic Josephson junctions seems to be the intrinsic
overheating at high bias.

Almost all high temperature superconductors have a low thermal conductivity,
which easily makes them overheated locally. For instance, taking the thermal
conductivity k ~10-2 Wcm-1K-1,
geometrical factor L~10-3 cm (assuming the typical area
S of mesa ~100 µm2 and the thickness of a single
crystal L~10µm), we obtain the thermal conductance of about
10-5 WK-1. Even for a low dissipation level of about
1 mW (for I» 3 mA and V»300mV, corresponding to the sum-gap voltage
of about 10 IJJ) we immediately have the overheating dT~100K.

The figure above demonstrates results of solving 2D-nonlinear heat (diffusion)
equation, in which both the temperature dependence of the thermal conductivity
and its anisotropy have been taken into account. The temperature dependence
was taken from experiment (see Physica C 169, 174 (1990)). It
is seen that for 5 W mm-2 of dissipated power density, the overheating
may be as high as 50 K, confirming the above mentioned estimate. Since
it is the power density, rather than power, which is important, to decrease
the sample sizes is meaningless. Even in STM- measurements, it may
be relevant, and should be considered with care.

The overheating is one of possible reasons for the "back-bending" of I-V-characteristics
at high bias current, see Figure. When
the temperature of the stack is increasing with bias current and approaches
Tc, the temperature dependent energy gap parameter becomes
smaller. Accordingly, the sum-gap voltage decreases also. The experimentally
obtained reduced 2D» 25meV may therefore
be a result of trivial overheating.

Possible applications. Three-terminal devices.

Since the 1950's, when study of the superconducting three-terminal devices
started with cryotrons, much attention has been paid to their development
(Bremer). The interest in superconducting transistors is due to their potential
advantages, like the ability to sustain high controllable current densities
without energy dissipation. Moreover, superconducting transistors are compatible
with other superconducting components, and may be required to interface with
superconducting electronics. Research on the superconducting transistors has
been intensified since the discovery of HTS, which opened ways of making relatively
cheap devices operating at liquid nitrogen temperatures. There have already
been made many attempts to fabricate different types of HTS transistors (Mannhart,
Claeson). The main types of superconducting transistors are: Josephson vortex
flow transistors , electric field-effect devices (SFETs), and quasiparticle-injection
devices. They have been shown to work at liquid nitrogen temperatures and
to have finite current or voltage gains.

Intrinsic Josephson junctions have an attractive feature of their SIS-
character of current-voltage characteristics, which opens up roads for possible
application like making heterodyne (SIS) mixers. The wider energy gap of
the high-Tc material may increase the operation of SIS mixers
up to about 5 THz. Other interesting features are the extremely small thickness
of the electrodes of each junction and the easiness of making stacks of different
areas and heights. The latter is in a favorable contrast to all other types
of high-Tc Josephson junctions, for which the fabrication of stacked
planar structures has always been a problem. This makes this material promising
for three-terminal devices, as will be explained below.

Quasiparticle-injection devices

The principle of such devices refers to the injection of non-equilibrium
quasiparticles into the drain-source (DS) channel from the control electrode
through a tunnel junction or weak link, formed on top of the DS channel. The
interest for these devices arises from a potential current gain and a fast
response time due to the creation of a non-equilibrium state. The characteristic
times of the relaxation of such a state is of the order of 1-100 ps (Mannhart).

Figure (a) schematically shows the assumed arrangement of such a device
with intrinsic Josephson junctions. The thickness of the electrodes, which
make the Josephson junctions in the Bi-2212 single crystals is extremely thin,
3 Å. This means, that the injected high-energy quasiparticles can penetrate
several unit cells deep into the Bi-2212 single crystal from its surface
and influence the properties of many intrinsic Josephson junctions connected
in series. This promise to increase the sensitivity and performance of a
device involving many IJJ.

The change of the density of quasiparticles dn=n-n0(T)
due to the current injection is:

dn=jt/ed

where j is the injection current density, t is the effective recombination time, e
is the electron charge, d is the quasiparticle penetration depth,
n is the total density of quasiparticles, and n0(T)
is the thermally excited density of quasiparticles. Taking j~103
Acm-2, d~10-100 Å, corresponding to the mean free
path of quasiparticles, and t~1-100 ps, we get dn~1010-1011 cm-3.
This value has to be compared with n0(T). For a
BCS superconductor, this number is exponentially decaying with decreasing
of temperature, n0(T)µ
exp(-D/T). To get n0(T)
of the same order of magnitude as dn, one
has to work at low temperatures. Estimations show that the temperature should
be less than 20-30 K for such a quasiparticle-injection device to work. The
most indefinite parameter in this consideration is the effective recombination
time t and the mean free path of quasiparticles.

For quasiparticles injected at much higher, than D
energies this time involves the electron-phonon relaxation and phonon escape
times due to the avalanche-like creation of the secondary quasiparticles,
including phonons. These times are usually several orders of magnitude higher
than t~1-100 ps, used for the above estimation.
This may drastically improve the low-frequency characteristics of the device
at high temperatures ~70 K, but, unfortunately, decrease the cut-off frequency
down to 1 - 10 GHz. One should therefore find the optimum between speed,
working temperature, and responsivity of the device. The parameter to change
is simply the thickness of the insulation layer between control electrode
and the stack of intrinsic Josephson junction. The thicker the layer the
higher is energy of the injected quasiparticles and the more avalanches of
the secondary quasiparticles are generated, which makes the responsivity
higher. This however may slow down the speed as it takes longer time to get
rid of all these quasiparticles afterwards for restoring the initial state.
The Bi-2212 IJJ are hysteretic at low temperatures and one can possibly make
use of this feature by fabricating switching devices also. Number of junctions
N which can feel the injected quasiparticles may be of the order of
10-100, so the output voltage of such a device can be 2DN~0.1-1 V without additional amplification.

Electric field-effect devices.

An electric filed applied to a superconductor via an insulating barrier
changes the density of the Cooper pairs in a thin layer of the depth d
of the superconductor close to the superconductor-insulator interface. As
the pair potential of the superconductor is a function of the Cooper pair
density, all superconducting properties in the field-penetrated layer depend
on the applied electric field. The characteristic length, which has to be
compared to the field-penetrated depth d is the superconducting coherence
length x . The condition d³x(T) should be satisfied for the effect
of the applied field be seen in the superconducting properties of the DS
channel. In the majority of high-Tc superconductors, d
is of the order of 1-10 nm (Frey95, Mannhart96) and x
(T) is of the same order, in contrast to low-Tc ones, for
which d<<x (T), and the field effects
are small.

The arrangement of the suggested IJJ-FET transistor is the same as for
the quasiparticle-injection one. The only difference is that the insulation
layer between the control electrode and the stack should be made much thicker
to have basically no input current between the two. This is promising for
achieving a high current gain. Intrinsic Josephson junctions incorporated
in such a type of devices favorably feature in comparison to all other high-Tc
junctions by their planar layered structure and their having a short coherence
length in the c-axis direction. As compared with the previous work
(Frey95), the suggested IJJ-FET is more feasible because all affected by
the electric field junctions contribute to the output voltage, and even one
of IJJ is enough for the device to be operate.

Moreover, in the usual in-plane geometry (Frey95, Mannhart96), the superconducting
sheets which are further away from the gate electrode and which are less affected
by the field, just short electrically the "useful" ones. Therefore the field-response
of thick layers of HTS material is basically much smaller than that for a
thin layer ~10 nm.

Josephson vortex flow transistors

In such devices, a drain-source (DS) channel is formed by a long Josephson
junction or by a number of short Josephson junctions connected in parallel.
The control line is usually put close to the channel, and the magnetic field
induced by the current in the control line generates Josephson vortices in
the junction. The vortices suppress the critical superconducting current Ic
of the junction, and once they flow under the influence of the drain-source
current IDS, they change the junction
resistance. Such transistors could have excellent decoupling of the input
circuit from the output one and no may operate at frequencies of the order
of 500 GHz (Mannhart). A simplified schematics of the suggested device is
drawn in Figure (b). There is a stack of 10 - 100 intrinsic Josephson junctions
with contacts on the top and near the base of the stack (drain and source).
The lateral dimensions are chosen with a big aspect ratio to form the so
called "long" Josephson junction with the in-line geometry. Dimensions of
the stack, which can be used for estimations are 100x2x0.05 µm3.
There is also a control line on top of the stack, made from a thin metal
film, and which is electrically isolated from the stack. In this geometry,
the control current Icont applied to the line produces
a magnetic field, which, once becoming larger than the first critical field
Hc1, generates the Josephson vortices in the stack. Hc1»10 G for the Bi-2212 material. This value agrees
with experiments on vortex flow in long stacks of IJJ (Lee95).

The current Icont in the control line, which is needed
to induce such a magnetic field in the stack may also be estimated from the
formula 4pIcont/cw, where
c is the velocity of light and w is the width of the control
line. Taking w~2µm, we get Icont~1 mA. This
means that just small currents are sufficient to control the vortex motion
in the stack for the simplest geometry of the device. To further improve
the sensitivity of the device one can use several layers of the control line
forming a multi-turn flat coil. It will increase the sensitivity but will
at the same time increase the input inductance and slow down the device.
The optimum matching to the external circuits must be found at high frequencies.